James F. Woodward has made a prediction, based on Sciama's formulation of Mach's Principle in the framework of general relativity, that in the presence of an energy flow the inertial mass of an object may undergo sizable variations, changing as the second time derivative of the energy. We describe an attempt to test for the predicted effect with a charging capacitor, using a technique that does not require an unbalanced force or any local violation of Newton s 3rd law of motion. We attempt to observe: (1) the gravitational effect of the varying mass and (2) the effect of the mass variation on a driven harmonic oscillator with the charging capacitor as the oscillating mass. We report on the predicted effect, the design and implementation of the measurement apparatus, and initial experience with the apparatus. At this time, however, we will not report on observations of the presence or absence of the Woodward effect.